Data-Centric Heterogeneous Catalysis: Identifying Rules and Materials Genes of Alkane Selective Oxidation

Artificial intelligence (AI) can accelerate catalyst design by identifying key physicochemical descriptive parameters correlated with the underlying processes triggering, favoring, or hindering the performance. In analogy to genes in biology, these parameters might be called “materials genes” of heterogeneous catalysis. However, widely used AI methods require big data, and only the smallest part of the available data meets the quality requirement for data-efficient AI. Here, we use rigorous experimental procedures, designed to consistently take into account the kinetics of the catalyst active states formation, to measure 55 physicochemical parameters as well as the reactivity of 12 catalysts toward ethane, propane, and n-butane oxidation reactions. These materials are based on vanadium or manganese redox-active elements and present diverse phase compositions, crystallinities, and catalytic behaviors. By applying the sure-independence-screening-and-sparsifying-operator symbolic-regression approach to the consistent data set, we identify nonlinear property–function relationships depending on several key parameters and reflecting the intricate interplay of processes that govern the formation of olefins and oxygenates: local transport, site isolation, surface redox activity, adsorption, and the material dynamical restructuring under reaction conditions. These processes are captured by parameters derived from N2 adsorption, X-ray photoelectron spectroscopy (XPS), and near-ambient-pressure in situ XPS. The data-centric approach indicates the most relevant characterization techniques to be used for catalyst design and provides “rules” on how the catalyst properties may be tuned in order to achieve the desired performance.


Catalyst Synthesis Procedures
MoVOx. 28 116.31 g of ammonium heptamolybdate (0.65 mmol Mo, Merck, purity >99%, Lot: A578482622) were dissolved in 2.875 L deionized water, which was obtained from a laboratory purification system (MilliQ), and mixed with 37.26 g VOSO4 (0.17 mmol V, Sigma-Aldrich, purity 97%, Lot: MKCB3411) dissolved in 375 mL water at ϑ = 30°C. The mixture was then transferred into a fully automated autoclave (MED1852, Premex Reactor AG, Switzerland) made of Hastelloy HC22 with a total volume of 5 L and a maximal operational volume of 3.75 L. The mixture was heated to ϑ = 200°C at 1°C/min and kept isothermal for 17 h while stirring with a rate of 100 rpm (lidheating off). The resulting black solid was isolated by filtration (pore 4 frit), washed 2 times with H2O and dryed at ϑ = 80°C for 16 h. 71.6 g of a black powder were obtained. The sample was washed with oxalic acid (0.25 mol/L, ϑ = 60 °C, 30 min, 25mL/g) and H2O and dried at ϑ = 80 °C for 24 h. Subsequently, a thermal treatment in Ar was performed (heating rate 10°C/min, 400°C, 2h, flow rate 100 mL/min) in a rotating furnace (Xerion, Germany) in portions of 2 g each. The activated portions were combined after confirming reproducibility by XRD, nitrogen adsorption and chemical analysis, and pressed and sieved according to the handbook, 29 sieve fraction 100-200 micrometer.
MoVTeNbOx. 30  VPP. 34 Vanadyl(IV) pyrophosphate (VPP, (VO)2P2O7) was synthesized according to patent literature following an organic route. In short, divanadium pentoxide (V2O5) as vanadium source was dissolved in isobutanol (C4H10O) and phosphoric acid (H3PO4) was added. The mixture was heated under reflux until the precursor was formed as precipitate, which was then filtered, washed, dried, and tempered. The powder was pressed and sieved according to the handbook, 29 sieve fraction 100-200 micrometer.
a-VPP. The synthesis of vanadyl(IV) pyrophosphate (VPP, (VO)2P2O7) in its amorphous phase was performed with the same approach, as described for VPP. The resulting precursor was filtered, washed, dried and pre-activated in wet lean air (5 % O2, 50 % steam in N2) at ϑ = 375 °C. The obtained powder was pressed and sieved according to the handbook, sieve fraction 100-200 micrometer.
β-VOPO4 35 The sample was synthesized in one batch according to the following procedure: 24.46 g of ammonium metavanadate (NH4VO3, Alfa Aesar, Lot L32044) was used as vanadium-source and mixed with 20.56 g diammonium hydrogenphosphate ((NH4)2HPO4, Roth, Lot 219284319). The mixture was then dissolved in 500 mL deionized water. 4 mL of nitric acid (HNO3, Thermo Fisher Scientific Inc., Lot 1864022) was added as an oxidizer. The solution was evaporated till dryness at temperatures ϑ ≤ 80 °C; while stirring at 300 rpm. The dry residue was then dried at ϑ = 120 °C for 16 hours. The obtained powder was exposed to multiple tempering steps (ϑ = 400 °C for 24 hours, ϑ = 500 °C for 24 hours, ϑ = 600 °C for 24 hours, ϑ = 725 °C for 24 hours). The obtained sample (30 g) with a yellow appearance was pressed and sieved according to the handbook, 29 sieve fraction 100-200 micrometer.
α-(V0.8W0.2)OPO4. 22,35 The sample was synthesized via solution combustion synthesis (SCS) in several small batches according to the following procedure: For each batch, 1.49 g of ammonium metavanadate (NH4VO3, Alfa Aesar, Lot L32044) was used as vanadium-and 0.8 g of ammonium metatungstate ((NH4)6W12O39, Alfa Aesar, Lot S05E020) as tungsten-source, which were mixed with 2.1 g diammonium hydrogenphosphate ((NH4)2HPO4, Roth, Lot 219284319). The mixture was dissolved in 80 mL deionized water followed by the addition of 3.58 g glycine (C2H5NO2, Sigma, Lot SLBV5094) as chelator and fuel. Furthermore, 2 mL of nitric acid (HNO3, Thermo Fisher Scientific Inc., Lot 1864022) was added as an oxidizer. The solution was evaporated till dryness at ϑ ≤ 80 °C while stirring at 250 rpm. The dry residue was then ignited in a preheated furnace at ϑ = 400 °C for 15 minutes. Then a first tempering step at ϑ = 400 °C was performed for 24 hours resulting in 43 g powder, which was then exposed to multiple tempering steps (ϑ = 500 °C and ϑ = 600 °C for 24 hours each and ϑ = 700 °C for 48 h). The obtained powder with an green appearance was pressed and sieved according to the handbook, 29 sieve fraction 100-200 micrometer.
V0.167W0.5P0.333O2.5+x. 36 The sample represents a novel tungsten-phosphate with a ReO3-like structure type. For a sufficient batch size, 2 batches were prepared. Each batch was synthesized according to the following procedure: 1.94 g of ammonium metavanadate (NH4VO3, Alfa Aesar, Lot L32044) was used as vanadium-and 12.54 g of ammonium metatungstate ((NH4)6W12O39, Alfa Aesar, Lot S05E020) as tungsten-source, which were mixed with 4.38 g diammonium hydrogenphosphate ((NH4)2HPO4, Roth, Lot 219284319). The mixture was dissolved in 400 mL deionized water followed by the addition of 15.94 g glycine (C2H5NO2, Sigma, Lot SLBV5094) as chelator and fuel and by 10 mL of nitric acid (HNO3, Thermo Fisher Scientific Inc., Lot 1864022) as an oxidizer. The solution was evaporated till dryness at ϑ ≤ 80 °C while stirring at 250 rpm. The dry residue was then ignited in a preheated furnace at ϑ = 400 °C for 15 minutes. Then a first tempering step at ϑ = 400 °C was performed for 16 hours. Two batches of 15 g powder each (∑ = 30.3 g) were obtained. The batches were combined and exposed to multiple tempering steps (ϑ = 500 °C for 16 hours, ϑ = 650 °C for 36 hours). The obtained powder with an olive green appearance was pressed and sieved according to the handbook, 29 sieve fraction 100-200 micrometer.
VOPO4·2H2O and αII-VOPO4. 37 After cooling it down to room temperature while mixing, the suspension was filtered (P3) and washed three times with 200 mL deionized water and dried. Then, the precipitate was washed three times with 100 mL acetone and dried at ϑ = 100 °C resulting in VOPO4·2H2O. To obtain the αII-phase, 17 g of the sample was used as precursor and tempered at ϑ = 725 °C for 2.5 days. The two different powders with a lemon-yellow appearance were pressed and sieved according to the handbook, 29 sieve fraction 100-200 micrometer.
Each sample is uniquely identified by a sample number in order to unambiguously assign reproductions of the synthesis. Table S2 gives an overview of the sample numbers of the freshly synthesized samples as well as the samples after activation and after the catalytic test in C2, C3 and C4 oxidation.

Functional Analysis and Ex Situ and In Situ Catalyst Characterization
The general catalyst characterization and testing procedures are described in the handbook , 29 whose updated version is accessible via the link https://ac.archive.fhi.mpg.de/P51850. More details are given below. The parameters varied and the data measured in the kinetic analysis are summarized in Figure 3 in the main text, in Table S3 and in Figures S3-S14. The materials properties measured are listed in Table S4.
Oxidation of Ethane and n-Butane. The catalyst tests were performed using a commercial 8-fold parallel setup build by hte GmbH. Catalyst volumes of 0.7 ml were placed in the isothermal zone of stainless steel reactor tubes with a diameter of 7 mm (the exact catalyst mass is documented with the data set). The catalyst bed was fixed by two inert steatite fillings. Reactor temperatures were individually controlled between 225 and 450°C at atmospheric pressure. The input gas feed was equally distributed between the parallel reactors. The feed composition was balanced by nitrogen. Argon was used as an internal standard, which included possible gas expansion in the data evaluation. The flow rates controlled by multiple mass flow controllers (MFC, Smart Mass Flow DELTA, Brooks Instrument LLC) were set based on the GHSV and feed composition guidelines of the respective reaction according to the handbook using C2H6, C2H4, C4H10 (purity 3.5), C4H8 (purity 2.0), O2 (purity 5.0), Ar (purity 5.0) and N2 (purity 5.0) (Westfalen AG, Air Liquide S.A.). The design of experiments was fixed using the handbook guidelines. A blank reactor filled with an inert material was used to monitor the exact input feed composition in parallel to the eight reactor measurements, that was applied as a reference in the calculations of conversion and selectivity. The outlet gas flows were consecutively analyzed using an online gas chromatography (GC) system (Two GC 7890 A, Agilent, column configurations including a combination of Restek RTX Wax, Agilent CP Volamin or Restek RTX-5, Agilent Doppel Saeule HR, HP-Plot8/Q+PT with a flame ionization (FID) and thermal conductivity detector (TCD) each). Based on the catalyst and the reactants, multiple products including MAN, acrylic acid, acetic acid, acetaldehyde, alkenes, alkanes, CO and CO2, among others, together with N2, O2 and Ar were identified and quantified. Each measurement point of the procedure or setpoint was tested in five iteration GC measurements. The final data set includes the averaged performance parameters at each setpoint. The overall gas composition was checked by a closed calculated carbon balance. The evaluation of the raw GC data was done using the commercial software tool myhte TM . The calculation was performed according to the handbook guidelines using the formulas given in the handbook.
Oxidation of Propane. The catalyst tests were carried out using three different setups: a single tube fixed-bed reactor setup (quartz reactor, ID = 8 mm), a setup with 8 fixed-bed tubular reactors in parallel (quartz reactors, ID = 8 mm) (ILS, Germany) and a setup with 10 fixed-bed tubular reactors in parallel (hastelloy reactors, ID = 2 mm) (ILS, Germany). The experiments were performed at atmospheric pressure and under steady state conditions. The catalyst bed was fixed in the isothermal zone of the corresponding reactor by two quartz wool plugs or inert ceramic frits, respectively. An appropriate volume of the catalyst was used to realize gas hourly space velocities from 1000 to 4000 h -1 . The exact catalyst mass is documented with the data set. The reactor temperatures were individually controlled between 225 and 450°C for the single-tube and the 10-fold parallel reactor and in two blocks of four reactors each for the 8-fold parallel reactor. The gasous reactant feed was mixed with mass flow controllers (EL-FLOW, Bronkhorst) using C3H8 (purity 3.5), C3H6 (purity 3.5), O2 (purity 5.0), and N2 (purity 5.0) (Westfalen AG). Steam was added to the gas flow through vaporizers. The design of experiments was fixed using the handbook guidelines. Gas analysis was done using 3 online gas chromatographs (Agilent 7890A) with an equal column configuration. A combination of Plot-Q and Plot-MoleSieve 5A columns, connected to a thermal conductivity detector (TCD), was used to analyse the permanent gases CO, CO2, N2, and O2. A system of a FFAP and a Plot-Q column, connected to a flame ionization detector (FID) with upstream methanizer, was used to analyse hydrocarbons, oxygenates, CO, and CO2. Each measurement point of the procedure or setpoint was tested in three to five iteration measurements. The final data set includes the averaged performance parameters at each setpoint. The overall gas composition was checked by a closed calculated carbon balance. The calculation was performed according to the handbook guidelines using the formulas given in the handbook.  corresponds to a different value for each of the three considered reactions, as the activation procedures are reactions conditions are reactiondependant. c In situ measurement under reaction conditions. The subscripts "dry", "wet" and "alkane" correspond to the three different reaction feeds applied at ref : dry feed, wet feed and alkane-rich feed, respectively.
CO Oxidation. CO oxidation measurements were carried out using a single tube fixed-bed reactor setup with a u-shaped quartz reactor at atmospheric pressure. An on-line gas analyzer (X-Stream, Emerson/Rosemount) was used for quantification of O2, CO, CO2 and H2O. The temperature inside the catalyst bed was recorded with a K-type thermocouple. The reactant feed was composed of CO, O2, and N2 as diluent. The CO-gas line was equipped with a carbonyl trap (tube filled with SiC and heated to 300 °C) and a CO 2 trap. All catalysts were pressed, crushed and sieved to a particle size of 100 to 200 µm. An appropriate volume of catalyst was used to realize a space velocity of 60000 h -1 (based on the undiluted catalyst). Each catalyst was diluted with SiC (100 to 200 µm) with a ratio of 1:9. All measurements were performed with a heating rate of 1 K min -1 . Prior to the CO oxidation, every fresh catalyst was pretreated at 150°C for 2 hours in inert gas flow. All CO oxidation measurements were performed from 30 °C to 420°C. Heating and cooling was repeated 3 times in the same feed (3 cycles Chemical Analysis. The chemical composition of the catalysts was determined by X-ray fluorescence spectroscopy using a Bruker S4 Pioneer wavelength dispersive X-ray fluorescence spectrometer. For sample preparation, a mixture of 0.05g of the catalyst and 8.9 g of lithium tetraborate (>99.995%, Aldrich) was fused into a disk using an automated fusion machine (Vulcan 2MA, Fluxana). The binary oxides were used for calibration.
X-ray Diffraction. X-ray diffraction (XRD) patterns were measured on a Bruker AXS D8 ADVANCE Series II theta/theta diffractometer, using Ni-filtered Cu Kα radiation and a position-sensitive LynxEye silicon strip detector. Powder samples were measured as provided (sieve fraction), i.e. without additional grinding, using a low background Si single crystal sample holder with a cavity. The data were collected in Bragg-Brentano geometry with a fixed 0.3° divergence slit (goniometer radius 217.5 mm) between 5 and 100° 2θ with 0.02° stepsize and a nominal counting time of 1 second/step, leading to a total accumulation time of 192 seconds per data point (due to 192 active detector channels). Identification of secondary phases was performed using DIFFRAC.EVA software (Bruker AXS) combined with the latest edition of the PDF-4+ database. The diffraction data were then analyzed by Whole Powder Pattern Fitting using the Rietveld method implemented in the DIFFRAC.TOPAS software (V5, Bruker AXS). The necessary crystal structure models were taken from the ICSD database unless noted otherwise. While lattice parameters, peak profile parameters, phase fractions and, in some cases, preferred orientation were refined, the atomic coordinates were generally kept fixed.
Temperature-Programmed Oxidation (TPO) and Temperature-Programmed Reduction (TPR). Temperature-programmed reduction and oxidation cycles were performed using a custom-designed TPR/O setup in a U shaped fixed bed quartz reactor (OD=10 mm, WT=1 mm). Around 300-350 mg pressed and sieved sample (100-200 micrometer) was positioned between two quarzwoll layers supported on the quartz substrate. All samples were exposed to sequential TPO-TPR cycles to examine the oxygen exchange capacity up to 400°C and its reversibility according to the following conditions: heating rate 5 K/min, 2 h holding time at 400°C, flow rate 40 mL min -1 , 0.25% O2 in He in TPO, 0.25% H2 in Ar.
The atmosphere in the cooling segment was the same as in the previous heating segment. The H2 and O2 consumption was monitored with thermal conductivity and paramagnetic detectors, respectively, build into a multichannel X-stream Gasanalyser by Emerson GmbH. An IR detector downstream of the O2 sensor (ABB EL1020) was used to detect CO2 during oxidation and inert treatment. A tube containing molecular sieve A was installed upstream the TCD detector as a water trap. The O2 and H2 detectors were calibrated with certified calibration gas mixtures and controlled with a CuO standard. The controlled gas flow was set with mass flow controllers EL-Flow by Bronkhorst calibrated with a flowmeter Definer 220. The gases used in the experiments (Ar (99.999%) and He (99.999%), Westfalen AG) were purified with Oxysorb and Hydrosorb cartriges. The inert segment was used to remove adsorbed species accumulated by contact with the ambient atmosphere. Nevertheless the first TPO segment was accompanied by significant CO2 evolution. Hence, only the second and third TPR/TPO cycles were considered for evaluation of the reversible oxygen release/uptake. Laboratory X-ray Photoelectron Spectroscopy (XPS). XPS spectra were recorded at room temperature using nonmonochromatized Al Kα (1486.6 eV) or Mg Kα (1253.6 eV) excitation and a hemispherical analyzer (Phoibos 150, SPECS). Instrument work functions were calibrated to give an Au 4f7/2 metallic gold binding energy (BE) of 83.95 eV, while the spectrometer dispersion was adjusted to give a BE of 932.63 eV for metallic Cu 2p3/2. Furthermore, the binding energy scale was calibrated by the standard Au 4f7/2 and Cu 2p3/2 procedure. To calculate the elemental composition, the theoretical cross sections from Yeh and Lindau, 39 the inelastic free path of the electrons from Tanuma, Powell and Penn, 40 and the transmission function of the analyzer were used.
Near-Ambient Pressure XPS (NAP-XPS). Ambient-pressure X-ray photoelectron spectroscopy measurements were performed at the BELChem facility at the synchrotron radiation light source BESSY II of the Helmholtz-Zentrum Berlin, Germany. The station is served by the UE56/2-PGM beamline as a monochromatic X-ray source. The details of the beamline layout and performance can be found elsewhere. 41 The home-built near-ambient pressure electron spectrometer was described in detail before. 42, 43 15 mg of the power samples were pressed into self-sustaining pellets and placed in front of the entrance aperture (diameter: 300 m) of the electron spectrometer. The gases where dosed via calibrated mass flow controllers to the XPS chamber. The total pressure was 250 Pa. Heating was provided by a NIR laser (LIMO GmbH) from the rear and the temperature was measured with a K-type thermocouple pressed onto the sample surface. A constant heating ramp of 5 K/min was applied. First, the samples were activated in oxygen, heated to 300°C in dry feed (9:3:20=O2/Cx/He) and the set of spectra was measured. After that the temperature was increased to various levels corresponding to the temperature of 30 % conversion in the reactor tests ("T30", temperature range between 300°C and 450°C). The feed gases were sequentially switched from wet feed (9:3:20=O2:Cx:H2O), back to dry feed (9:3:20= O2:Cx:He), and finally to Cx rich feed (3:9:20=O2:Cx:He). During each treatment step a set of core level spectra, valence band spectra, and secondary electron cut-off spectra has been measured after an equilibration time of 30 min. Core level spectra were recorded with a constant kinetic energy of about 150 eV by adapting the photon energy accordingly. This results in probing the outermost surface region with an inelastic mean free path of approximately λ = 0.6 nm for these materials. 44,45 The pass energy of the hemispherical analyzer was 20 eV, the exit slit of the beamline 180 m. For the quantitative analysis of the core levels, atomic subshell photoionization cross sections and asymmetry parameters from numerical calculations by Yeh and Lindau were used taking the photon-energy-dependent photon flux into account. 39 The core-level spectra were deconvoluted to determine the oxidation state using Gaussian− Lorentzian product functions after subtracting a Shirley background with the CasaXPS software. 46 To determine the work function of the sample, the secondary electron cut-off was measured with a bias of −17.8 V applied to the sample at a photon energy of 100 eV, beamline exit slit of 20 m -40 m, and a pass energy of 2 eV. The position of the cut-off was determined by a linear extrapolation between 20 and 80% of the maximum intensity. The valence band (VB) onset was likewise evaluated by a leading-edge extrapolation using a photon energy of 100 eV. The composition of the effluent gas from the XPS cell was analyzed with a Thermo Scientific TRACE 1300 gas chromatograph to evaluate conversion and product selectivity.

Details on the Artificial-Intelligence Analysis
We used the SISSO++ code 47 with 200 SIS-selected descriptors per dimension ( ) for model identification via the SO. Ten different residuals per dimension were considered to select these descriptors in the case of models with > 1. The following mathematical operators were used: addition, (absolute) difference, multiplication, division, exponential, power (2, 3 or 6), square and cubic roots, logarithm and absolute value. Because the size of the descriptor candidate space grows in a combinatorial way with the number of primary features and mathematical operators, we only used part of the initial primary features for the identification of descriptors with rung 3 ( = 3). This is to keep the descriptor identification computationally feasible. We chose the primary features that appear in the top-ranked descriptors at the optimal complexity identified considering only = 1 and = 2 (Table S5). For the case of models trained with fresh-catalyst data only, all 16 primary features were consider in the = 3 analysis. The AI approach is discussed in further details in a previous contribution. 48 In order to evaluate the optimal model complexity, we performed leave-one-material-out cross-validation. This CV procedure consists of training models with a data set in which one of the catalysts is removed, and then using the so-obtained ensemble of best models to predict the property of the left-out material. This procedure is iterated until all the catalysts are left-out once. The root mean squared errors (RMSEs) averaged over all CV iterations (averaged CV-RMSEs) are used as our performance metric. The optimal complexity is considered the one with the lowest CV-RMSE. Because of the rather small number of materials and the fact that some materials might be unique compared the remaining ones (e.g., MoVTeNbOx in C3 oxidation), the estimation of the target for the left-out material using the best model trained on the remaining materials might present abnormally low or high values, for example due to small denominators on the descriptor expression. This is particularly the case for higher-rung and higher-dimensional models. To circumvent this issue, we considered, for the evaluation of CV-RMSE, not only the best model, but rather the few ensemble best top-ranked models (ranked according to their training RMSE) when estimating the RMSE on the left-out (test) material. By doing this, we ensure a balance between the performance on the subset of data used for training and on the test material. The evolution of CV-RMSE as a function of ensemble (Fig. S1) shows that when only the model with the best performance in the training set is considered ( ensemble = 1), the CV-RMSEs might be extremely large for some models. When a few more models are considered in the ensemble, the errors drop significantly and are stabilized for ensemble sizes of ca. 25 for most of the cases. The CV-RMSE values shown in Fig. S2 correspond to ensemble = 25. For the case of the target oxygenate , the CV-RMSE values for = 1 and = 2, 1-D models are very similar (1.89 and 2.03%, respectively, Fig. S2). Thus, both complexities could be considered optimal. We only discuss the = 2, 1-D model in the manuscript based on the fact that the CV-RMSE is stabilized at lower ensemble values for = 2 compared to = 1 (Fig. S1).
The descriptor associated to the best identified model for oxygenate with the complexity 1-D, = 1 model is | alkane − wet |.

Detailed Description of X-Ray Diffraction Characterization
The crystal structures and peak shape models used in the whole powder pattern fitting according to the Rietveld method are listed in Table S6.  The XRD patterns of MoVOx showed strongly "super-Lorentzian" reflections (i.e., sharp tips combined with very broad bases), indicating a rather wide domain size distribution. Accordingly, the Rietveld fits required the superposition of two MoVOx "phases" (with lattice parameters constrained to be identical), representing large and small domain sizes, to approximate the measured patterns reasonably well. In addition, the patterns exhibited strong preferred orientation effects with suppression of the 001 orientation. This observation is in line with the needle-like crystal morphology and demonstrates that the crystals were not agglomerated, as they responded readily to the gentle directing forces of sample preparation. In contrast, the isostructural MoVTeNbOx catalysts were highly crystalline, showed slightly anisotropic peak broadening, but lacked noticeable preferred orientation, thus indicating agglomeration of the needle-like crystals in random orientation. The diffraction patterns of MnWO4 exhibited distinctly anisotropic peak broadening, which was fitted using a modified Stephens model 59 adapted for size broadening. 31 The reflection profiles of the SmMnO 3 perovskite and V 2 O 5 were slightly anisotropic. The XRD patterns of crystalline VPP exhibited distinctly anisotropic peak broadening, which can be attributed to the presence of stacking faults. 60 Unfortunately, the effects of stacking faults on the diffraction pattern cannot be modeled satisfactory using conventional Rietveld methods. Hence, the best approximation available to us described the measured patterns only moderately well. "Amorphous VPP", which was actually found to contain some poorly crystalline hemihydrate VOHPO4·½H2O in addition to the amorphous component, crystallizes into (VO)2P2O7 during the oxidation of the alkanes. The latter shows the same stacking fault problems as the originally crystalline VPP catalysts. The reflections of β-and αII-VOPO4 were isotropic, while the XRD patterns of αII-(V,W)OPO4 were found to be very inhomogeneous, likely due to an uneven distribution of Mo and V throughout the sample. Correspondingly, the patterns could only be approximated by using two strongly overlapping phases based on (V0.74W0.26)OPO4 and (V0.9W0.1)OPO4, 35 both with anisotropic peak broadening. The VOPO4·2H2O diffraction patters proved to be particularly troublesome, as the layered hydrate loses water upon mechanical pressing (preparation of defined sieve fraction for catalysis) or heating (during catalytic reaction), causing stacking faults and a general degradation of the crystal structure. Dehydrated samples contained more or less crystalline αI-VOPO4, which represents the completely dehydrated state of VOPO 4 ·2H 2 O, formed by topotactic deintercalation of water. When exposed to ambient conditions, however, the samples re-hydrated to VOPO4·2H2O, again creating stacking faults which affected the αI-VOPO4 and VOPO4·2H2O patterns. Consequently, most samples were found to be VOPO4·2H2O/αI-VOPO4 mixtures during the XRD measurements, with strongly varying anisotropic peak broadening effects. While both VOPO4·2H2O and αI-VOPO4 were approximated using anisotropic peak broadening, the fits were typically not satisfactory. VWPOx, which can be described with the formula V0.167W0.5P0.333Ox, seems to have a ReO3-type structure, which was approximated using a cubic WO3 model with a mixed occupation of the metal site.
The diffraction patterns show discrete reflections on top of a diffuse background formed by very broad peaks, which seem to be centered around the crystalline reflections. Correspondingly, it was assumed that the diffuse peaks represent nanocrystalline material of similar composition as the crystalline VWPOx phase, and crystalline and diffuse component were both fitted with the same WO3 type structure and coupled lattice parameters, but vastly different nominal domain sizes. Surprisingly, the nanocrystalline component did not crystallize further under catalytic conditions. The broad diversity of structures and microstructural properties made a numerical assessment of the changes observed after the catalytic reactions difficult to impossible. The only numerical quantity, which is both accessible and comparable for all crystalline catalysts, is the relative change of the unit cell volumes, which is listed in Table S7 and visualized in Figure S16. Table S8 summarizes whether or not fresh and spent catalysts were single phase according to XRD. In those cases in which a single phase fresh catalyst is not phase pure anymore after reaction, it can be inferred that the main phase is not stable against phase transformation under the conditions applied. In contrast, if the starting material is already a phase mixture, no conclusions about the main phase stability can be made from Table S8 alone. Thus, Table S9 gives information about whether or not the main phase of a catalyst seems to transform under catalytic conditions. Table S10 lists the secondary phases of mixed phase catalysts, although it needs to be kept in mind that some of the phase assignments are only tentative. The observed diffraction peak profiles in the crystalline samples, and the models necessary to fit them, were too diverse (see Table S6) to allow a consistent numerical micro-structural characterization of all catalysts. However, an increase in peak broadening, independent from the actual nature of the defects, always indicates an increase in defectivity (i.e., smaller domain sizes, stronger mirco-strain, larger stacking fault concentration). Thus, we looked qualitatively at whether or not a catalytic reaction changed the peak broadening, with the results collected in Table S11. Some general trends which can be deduced are the following: All vanadium phosphates (V,W)OPO4 are phase mixtures, which undergo phase transformations during catalysis. The extent of phase changes depends on the reaction carried out. Generally, the αII modification is partially transformed into the β modification. The highly crystalline, phase-pure materials MoVOx, MoVTeNbOx, MnWO4, SmMnO3, V2O5, and VPP are also characterized by high structural stability under most conditions. Only MoVTeNbOx and especially V2O5 exhibited some loss of phase integrity under propane oxidation conditions (Tables S9 and  S10). Otherwise, there is no segregation of secondary phases after use, while changes in peak broadening and/or lattice parameters can be observed after the alkane oxidation reactions in many cases (Tables S7 and S11).  Table S7. Amorphous VPP is not included since the starting material has no defined unit cell. * In contrast to the remaining catalysts, where unit cell changes are likely related to changes in the oxidation state, the differences observed in VOPO4·2H2O are predominantly caused by the dynamic de-/re-hydration behavior and associated stacking faults.